Metalanguage . Language or symbols used in the language itself being discussed or examined.
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- 1 Definitions
- 1 In general terms
- 2 In logic and linguistics
- 3 Others
- 2 Types of metalanguage
- 1 Embedded Metalanguage
- 2 Order metalanguage
- 3 Nested metalanguage
- 3 Types of expressions in a metalanguage
- 1 Deductive systems
- 2 Other
- 3 Metavariables
- 4 Metatheories and metatheorems
- 5 Interpretations
- 4 Role in metaphor
- 5 Role of informatics
- 6 The use of metalanguages
- 7 Metalanguages and science
- 1 Formalized languages and model building
- 8 Source
In general terms
Any metalanguage is the language or symbols used in the language itself that is being discussed or examined .
In logic and linguistics
A metalanguage is a language used to make statements about statements in another language (it is a language that is used to talk about another language). Expressions in a metalanguage are often distinguished from those in an object language by using italics, quotation marks, or writing on a separate line.
- Other definitions of metalanguage as a formal technical language “.
- The metalanguage can be identical to the object language, for example when speaking about Spanish using Spanish itself.
- One metalanguage at a time can be the target language of another higher-order metalanguage, and so on. Different metalanguages can talk about different aspects of the same object language.
- In a more general sense, it can refer to any terminology or language used to speak with reference to the same language. For example, a text about grammar or a discussion about the use of language.
Types of metalanguage
There are a variety of recognized metalanguages, including embedded, ordered, and nested.
An embedded metalanguage is a formal language , naturally and firmly fixed in an object language. This idea is found in the book Gödel, Escher, Bach: an Eternal and Graceful Loop or Gödel, Escher, Bach: an eternal golden braid by Douglas Hofstadter , whose central theme is how the creative achievements of the logician Kurt Gödel, by the artist Maurits, interact Cornelis Escher and the composer Johann Sebastian Bach and whose use of formal language makes so many twists and turns that it recalls number theory: “so that. It is in the nature of the formalization of number theory that its metalanguage is embedded inside of her. ”
It occurs in natural or informal languages, such as in English , where descriptors, that is, adjectives , adverbs and possessive pronouns , constitute an integrated metalanguage, and where nouns , verbs and, in some cases, adjectives and adverbs , constitute a target language. Therefore, the adjective “red” in the phrase “red barn” is part of the embedded meta-language of English, the noun “barn” is part of the object language. In the phrase “little by little to run”, the verb “to run” is part of the object language, the adverb “slowly”
An ordered metalanguage is analogous to ordered logic. An example of an ordered metalanguage is the construction of a metalanguage to speak one object language, followed by the creation of another metalanguage to discuss the first one, etc.
A nested metalanguage is similar to an ordered metalanguage in that each level represents a greater degree of abstraction. However, a nested metalanguage differs from a request in that each level includes the one below. The paradigmatic example of a nested metalanguage comes from the Linnean taxonomic system in biology. Each level in the system incorporates the one below. The language used to discuss gender is also used to examine species; the one used to discuss orders is also used to discuss genders, etc, even kingdoms.
Types of expressions in a metalanguage
There are several entities commonly expressed in a metalanguage. In the general logic of the object language that the metalanguage is discussing is a formal language, and very often the metalanguage as well.
A deductive system of a formal system, is composed of the axioms and inference rules that can be used to obtain the theorems of the system.
Formal syntax models for describing grammar, such as generative grammar, are types of metalanguage.
A metavariable is a symbol or set of symbols in a metalanguage that represents a symbol or set of symbols in some object language. For example, in the sentence:
Let A and B be an arbitrary formula of a formal language.
Symbols A and B are not symbols of the object language, they are metavariables in the metalanguage that the object language is discussing. The convention is that within the same context, the same metavariable always represents the same element of the object language, but different metavariables do not necessarily represent different elements.
Metatheories and metatheorems
A metatheory is a theory whose object is another theory. Statements made in the metatheory of the theory are called metatheorems. A metatheorem is a true statement about a formal system expressed in a metalanguage. Unlike proven theorems within a given formal system, a metatheorem is proven within a metatheory, and can refer to concepts that are present in the metatheory but not the object theory.
An interpretation is an assignment of meanings to the symbols and words of a language.
Role in metaphor
Michael J. Reddy has discovered and demonstrated that much of the language we use to talk about language is conceptualized and structured, by what he refers to as the conduit metaphor. This paradigm operates through two distinct related frameworks.
The main framework views language as a sealed pipe between people:
- Thoughts and feelings Language transfers from people to others Example: Try to conceive your thoughts through a better one.
- Speakers and writers insert their mental content into example words: You have to put each concept into words more carefully.
- Words are example containers: That phrase was filled with emotion.
- Listeners and writers extract mental content from example words: I want to know if you find any new sensations in the poem.
The minor frame sees the tongue as an open tube spilling mental content into the void.
- Speakers and writers expel mental content in an outer space example: Get ideas by where they can do something good.
- Mental content is encoded in this example space: That concept has been floating around for decades.
- Listeners and writers extract mental content from this example space: Let me know if you find any good concepts in the essay.
Computers follow programs, sets of instructions in clear and simple language. The development of a programming language involves the use of a metalanguage. Backus-Naur Form , developed in the 1960s by John Backus and Peter Naur , is one of the first metalanguages used in computing.
The use of metalanguages
On many occasions we use this resource with which, if you are not aware, you can make errors of interpretation.
Already in the grammar a distinction is made between use and mention.
Bisílaba is any word that has two syllables. But ‘bisyllable’  is not bisyllable. In this case, ‘bisyllable’ refers to the word itself, not to its object meaning, that is, to a bisyllable word.
All language has an object to which it addresses or refers. It is the “language-object”.
Any language whose object is a language is a “metalanguage”, which in turn can be the object language of another higher order metalanguage, and so on.
Let us consider the different references of the following sentence: “Antonio says that Luis said that María Luisa said that …”
“Antonio said he went to the movies yesterday.” Note that such a statement does not give us information about whether or not Antonio went to the movies yesterday.
Not taking into account that distinction that speaks of the reality of the event: “Antonio said” and the language (metalanguage) about what Antonio said: “that he went to the movies yesterday” lends itself to interpretive confusion.
Metalanguages and science
In scientific language this distinction is of great importance.
The theory of language levels was established by Bertrand Russell in his introduction to Wittgenstein’s Tractatus Logico-Philosophicus.
Russell, who had developed the theory of types in order to solve some logical paradoxes, states that “each language has its own structure regarding which nothing can be stated in the language itself; but there may be another language that deals with the structure of the language. first language, there being no limits in this hierarchy of languages ”.
The distinction between object language and metalanguage was introduced by Alfred Tarski as a solution to semantic paradoxes such as the liar’s paradox.  According to Tarski, no language can contain its own truth predicate and remain consistent.  To speak about the truth in a language, and not generate contradictions, it is necessary to do so from a different language, with greater expressive power: the metalanguage. 
This is how the classic liar paradox is resolved. The grammatically correct expression: “Epimenides the Cretan says that all Cretans are liars” cannot have, nor does it have any truth value. But its sense of truth appears clearly when we distinguish two levels of language. “Epimenides the Cretan says:” All Cretans are liars “”.
Formalized languages and model building
But the study of metalanguage from the point of view of its “formal” or “syntactic” structure is of special relevance, which gives rise to formal logical-mathematical languages.
When we construct a formal language, with symbols and syntactic structures perfectly determined by the rules for constructing formulas, we can also use higher order variables to refer to the established formal language.
Such a procedure occurs in the substitution rule of the calculation, when we substitute an expression for a metavariable.
Thus are expressed, for example, the rules of calculation with metavariables substitutable by any well-formed expression of the language.
For example the expression
[(A → B) / \ A] → B can be considered a metalanguage with respect to the expression
[[(p / \ q) → (r \ / s)] / \ (p / \ q] → (r \ / s), where A = (p / \ q) and B = (r \ / s) .
In turn p, q, r, and s, can symbolize any proposition of ordinary language. When we give these variables a semantic content, we build a model based on a logical-mathematical calculation.
Also in arithmetic we use symbols, 0,1,2,3,4,5,6,7,8,9 that can each represent “a quantity of objects, or of measure”. In turn, in algebra we symbolize these numbers by letters, variables or constants, which can substitute for “quantities of objects, or measures”, as long as the rules of expression formation through syntactic relations, +, -, x, / , etc. are perfectly defined.
When in a calculation C, a “correspondence” of each symbol is established with individual determinate elements distinguishable from each other, of a real Universe L (such universe L is not an empty set, by the same conditions that we have established) THEN it is said that L is a MODEL of C. Example of truths whose referent is a language, not reality
The truth that Antonio went to the movies yesterday does not depend on what he said, but on the “fact” of experience that he went to the movies yesterday or not.
The conclusions of meteorologists easily fail in their forecasts because their conclusions are about very sophisticated scientific models, yes, but they do not cover far from all the variables of what reality is that speaks for itself.
The construction of models is a fundamental instrument in scientific research. But the truths obtained about the model do not have to always respond to reality. Frequently the truths obtained according to the model are confused with the truth of reality.
But the truths obtained from the model have as their “object referent” the formal language used, (generally representing a formalization with respect to a theory) and therefore these truths are a metalanguage that talks about the theory (consequences of it) not about reality. Reality will speak only through experimentation. 
Not taking this detail into account sometimes leads to affirming as real truths what are only truths obtained “according to the model”; what many media, and not always disinterestedly or by mistake, disclose them as if they were already consolidated scientific truths. [5
In order not to get caught up in such problems, it is interesting to distinguish the level of the target language from the metalinguistic level. By object language I understand that which I use to refer to something (objects, facts, relationships, properties, functions, ideas, values, imaginary objects, etc.) other than language itself. The metalanguage refers to the object language, but it is more “rich”, in the sense that it allows to refer to the truth values or the ways of meaning, of the statements of the object language.
The object language “says” or “uses” what the metalanguage “shows” or “mentions.” Can one speak of truth or falsehood of metalanguage? Of course, but we will have to use a meta-metalanguage, that is, a level 2 metalanguage that refers to the level 1 metalanguage. For example:
A: The exterior angles of a triangle add two straight lines B: Statement A is true C: Statement B is true D: Statement C is true
Statement A states a theorem about geometric objects. But a geometry manual containing proofs of the theorems will be written in at least a B-level metalanguage. Books dealing with proof theory are written in a C-level metalanguage. Fortunately, it is seldom necessary to go beyond the level C.
The metalanguages are arranged like those Russian dolls that contain each other. The object language would be the analogue of the smallest doll, one that does not contain more dolls within itself, but rather objective representations.
There are expressions such as “it is true”, “it is false”, “it is doubtful”, “it is necessary”, and so on. which almost always refer to statements: “it is true that Mars has two moons”, that is: the sentence “Mars has two moons” is true.
The distinction between language and metalanguage is parallel to the distinction between use and mention: we properly use language to refer to something that is not itself, using words as signs, whose signifier we use regardless of it, meaning is what we use. matters and its agreed relation to a certain image of what goes on in the world. But in statements such as “the expression ‘positive discrimination’ is a contradiction between the terms”, some of the words, in addition to being used, are being mentioned. Specifically: “positive discrimination”. We have used that expression to refer to herself. We use the quotation marks to indicate that we are not referring to the meaning of the expression but to the expression itself, which we consider incongruous.
E: “To love” is a verb with a very complex meaning. F: People who pretend to be psychologists pronounce the word “libido” as if it were esdrújula (like “livid”: pale, purple), but it is flat.
There are three possibilities:
1) Use a word without mentioning it: “Only time is ours” (Seneca). 2) Use it and at the same time mention it: “The word ‘leader’ comes from English”. 3) Mention it without using it: “the Spanish word with which we mean the domestic feline is written with four letters”.
Currently, every time we use a metalanguage we are using its expressions and, at the same time, we are using and at the same time mentioning the expressions of the object-language in question.
An example taken from propositional logic:
The expression “A => (A v B)” belongs to the metalanguage of propositional logic, and can be read: “formula A implies its logical sum with any other formula”. When I say this, I mean the conditional (->) that joins the first formula of the antecedent (A) with the second, complex formula of the consequent (A v B), to say that said conditional ((A -> (A v B )) is necessarily true, regardless of the truth value taken by A or B.